In order to ensure that the mask structures are imaged as precisely as possible onto the wafer, a projection lens having the lowest possible level of wavefront aberrations is desired. Projection lenses are therefore equipped with manipulators which make it possible to correct wavefront aberrations by changing the state of individual optical elements of the projection lens. Examples of such a state change include: a change in position in one or more of the six rigid body degrees of freedom of the relevant optical element, an application of heat and/or cold to the optical element, and a deformation of the optical element. Usually, for this purpose, the aberration characteristic of the projection lens is regularly measured and, if appropriate, changes in the aberration characteristic between the individual measurements are determined by simulation. In this regard, for example, lens element heating effects can be taken into account computationally. The terms “lens element warming”, “mirror heating” and “mirror warming” are also used synonymously for “lens element heating”. The manipulator changes to be carried out in order to correct the aberration characteristic are calculated via a travel generating optimization algorithm, which is also referred to as “manipulator change model”. Such optimization algorithms are described for example in WO 2010/034674 A1.
“Travel” is understood to mean a change—effected via manipulator actuation—in a state variable of an optical element along the travel for the purpose of changing the optical effect thereof. Such travel defined by changing a state variable of the optical element is specified by setpoint change variables of the manipulator. By way of example, the manipulation can consist in a displacement of the optical element in a specific direction, but also, for example, in an, in particular local or areal, application of heat, cold, forces, light having a specific wavelength or currents to the optical element. By way of example, in the case of displacement, the setpoint change variable can define a path length to be covered or an angular range to be covered.
Known travel generating optimization algorithms are often unsuitable for active manipulator control during the exposure of a wafer owing to excessively long computation times when establishing a travel command. The computation times of travel generating optimization algorithms can be reduced via Tikhonov regularization, for example. However, that can lead to a loss of accuracy in the result of the optimization process.